It made air combat more controllable, and put more use to sidestep dodges, as jumping no longer became a universal dodge move that was flying above all of the ground moves. Another big change in movement was that jumping was toned down, no longer allowing fighters to jump to extreme heights (as was present in previous games), but keeping leaps to reasonable, realistic heights.
Perhaps the most noticeable change from Tekken 2 fight system is movement reform - whereas the element of depth had been largely insignificant in previous Tekken games (aside from some characters having unique sidesteps and dodging maneuvers), Tekken 3 added emphasis on the third axis, allowing all characters to sidestep in or out of the background by lightly pressing the arcade stick (or tapping the controller button in the console version) towards the corresponding direction.